# Slurry Flow and Erosion Prediction in a Centrifugal Pump after Long-Term Operation

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## Abstract

**:**

## 1. Introduction

## 2. Mathematical Model

#### 2.1. Mathematical Model for Liquid Phase

#### 2.2. Mathematical Model for Particles

_{p}and ${\overrightarrow{U}}_{P}$ are the particle mass and velocities. ${\overrightarrow{F}}_{D}$, ${\overrightarrow{F}}_{P}$, and ${\overrightarrow{F}}_{VM}$ are the drag force, pressure gradient force, and virtual mass force for the particles.

## 3. Numerical Methods

#### 3.1. Pump Model

^{3}/h for the fluid, where the volume concentration for the particles is 5% under this condition. The flow components consist of a semi-open type impeller and a volute. The rotating speed is 1450 rpm, with a specific speed of 172. The Stokes number is defined as $St={\rho}_{f}{d}_{p}^{2}{V}_{s}/\left(18{\mu}_{f}{L}_{s}\right)$, where the characteristic length ${L}_{s}$ and velocity ${V}_{s}$ are the diameter of the impeller and the circumferential velocity at the impeller outlet in centrifugal pumps, respectively [36]. The particle Stokes number for the centrifugal pump is 0.0675, much smaller than 1, implying that the particles follow water closely. The flow is at a highly turbulent level, and the flow Reynolds number for the current pump is 5.08 × 10

^{5}.

#### 3.2. Mesh Generation

#### 3.3. Numerical Scheme and Boundary Conditions

#### 3.4. Numerical Models with Eroded Blades

## 4. Results and Discussions

#### 4.1. Pump Performances

#### 4.1.1. Pump Performances under Pure Water Conditions

_{d}for model A and model B. As illustrated in the graph, the performance of the pump is greatly reduced after the impeller wears, with a significant drop for the head and efficiency.

_{d}. In contrast, after the impeller is worn, the efficiency drops sharply after 0.8Q

_{d}. This is because the shape of the blade after wear is deteriorated, therefore changing the efficiency curve.

#### 4.1.2. Pump Performance under Two-Phase Conditions

#### 4.2. Particle Trajectories

#### 4.3. Erosion Patterns for the Pump

#### 4.3.1. Verification of Numerical Methods

#### 4.3.2. Evolution of Erosion Patterns for the Impeller

#### 4.3.3. Evolution of Erosion Patterns for the Volute

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 3.**Model comparisons: (

**a**) Model A; (

**b**) comparisons between the failed impeller and model B; (

**c**) Model B.

**Figure 4.**Model comparisons for a single blade from the side view (the yellow wireframe represents model A while the solid body is model B).

**Figure 7.**Particle trajectories in the impeller (

**a**), (

**c**) model A, and (

**b**,

**d**) model B (the red dash line qualitatively represents the location for the particle vortices).

**Figure 8.**Particle trajectories and the fluid streamlines of the continuous phase (

**a**) for model A and (

**b**) model B (the white line represents the fluid streamlines; the red dash line qualitatively represents the location for the particle vortices).

**Figure 9.**Results for model A with the actually worn impeller (the orange dashed line represent the positions for different blade spans).

**Figure 10.**Erosion rates of the impeller for model A. (

**a**) Pressure side and outlet edge (the outlet edge are near the position of R ≈ 0.2 m); (

**b**) suction side.

**Figure 12.**Erosion rates of the impeller for both models. (

**a**) Pressure side and outlet edge (the outlet edge is near the position of R ≈ 0.2m); (

**b**) suction side.

**Figure 14.**Erosion development for the volute for (

**a**) model A and (

**b**) model B. (

**c**) Erosion pattern for the actual volute (Noon, 2017 [28]).

Parameters | Descriptions |
---|---|

Slurry | Pulp and water (5% volume fraction) |

Slurry density | 75 kg/m^{3} |

Particles to fluids density ratio | 0.075 |

Mean diameter of particles | 0.5 mm |

Pump material | Stainless steel |

Model | Description | Radius/mm | Outlet Width/mm | Blade Thickness/mm |
---|---|---|---|---|

A | Model with unworn blades | 190 | 50 | 13 |

B | Model with slightly worn blades | 188 | 42 | 10 |

Model | Method | Efficiency/% | Head/m | Power/kW |
---|---|---|---|---|

Model A | With particle | 73.74 | 21.88 | 55.30 |

Pure water | 73.56 | 21.59 | 54.98 | |

Model B | With particle | 57.45 | 11.38 | 36.92 |

Pure water | 54.01 | 10.89 | 37.77 |

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## Share and Cite

**MDPI and ACS Style**

Xiao, Y.; Guo, B.; Ahn, S.-H.; Luo, Y.; Wang, Z.; Shi, G.; Li, Y.
Slurry Flow and Erosion Prediction in a Centrifugal Pump after Long-Term Operation. *Energies* **2019**, *12*, 1523.
https://doi.org/10.3390/en12081523

**AMA Style**

Xiao Y, Guo B, Ahn S-H, Luo Y, Wang Z, Shi G, Li Y.
Slurry Flow and Erosion Prediction in a Centrifugal Pump after Long-Term Operation. *Energies*. 2019; 12(8):1523.
https://doi.org/10.3390/en12081523

**Chicago/Turabian Style**

Xiao, Yexiang, Bao Guo, Soo-Hwang Ahn, Yongyao Luo, Zhengwei Wang, Guangtai Shi, and Yanhao Li.
2019. "Slurry Flow and Erosion Prediction in a Centrifugal Pump after Long-Term Operation" *Energies* 12, no. 8: 1523.
https://doi.org/10.3390/en12081523